I am running a Mixture model and I have no free parameters, I just have it evaluating for a given datapoint, its likelihood of belonging to one cluster. Separately, I have a ground truth about these values that the model never sees. I want to test whether the model successfully predict the data point clusters' likelihood. What metrics do you suggest are best for this? are cross entropy RMSE MAE and others good metrics?
(I know about the classical model comparison -e.g., BIC, AIC, WAIC CV_LOO and so on so fourth, but I am not testing whether my model is the best possible model, but whether it is able to predict the clustering)
